Analysis and modelling of MHD instabilities in DIIID plasmas for the ITER mission

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1 Analysis and modelling of MHD instabilities in DIIID plasmas for the ITER mission by F. Turco 1 with J.M. Hanson 1, A.D. Turnbull 2, G.A. Navratil 1, C. PazSoldan 2, F. Carpanese 3, C.C. Petty 2, T.C. Luce 2 1 Columbia U. 2 General Atomics 3 Dipartimento di Energetica, Politecnico di Milano IAEATM, Roma, March 6 th 2015
2 Contents  Making progress by integrating modelling and experiment à MHD spectroscopy to measure the approach to a limit à The MARSK model for plasma response calculations à The PEST3 model to evaluate Δ trends  The ITER Baseline Scenario: moderate β N, zero torque  The path to high β N and steadystate conditions à Modeling the nowall limit crossing with nonideal effects  The steadystate scenarios: high β N, high torque  Low torque at high β N  Discussion and conclusions
3 DIIID studies demonstration plasmas relevant to these scenarios: ITER Baseline Scenario (IBS) (RWM studies) ITER Steady State ITER I p (MA) 15 / 9 q Q 10 / 5 DIIID β N DIIID Torque (Nm)
4 DIIID studies demonstration plasmas relevant to these scenarios: ITER Baseline Scenario (IBS) (RWM studies) ITER Steady State ITER I p (MA) 15 / 9 q Q 10 / 5 DIIID β N DIIID Torque (Nm)
5 DIIID studies demonstration plasmas relevant to these scenarios: ITER Baseline Scenario (IBS) (RWM studies) ITER Steady State ITER I p (MA) 15 / 9 q Q 10 / 5 DIIID β N DIIID Torque (Nm)
6 DIIID studies demonstration plasmas relevant to these scenarios: ITER Baseline Scenario (IBS) (RWM studies) ITER Steady State ITER I p (MA) 15 / 9 q Q 10 / 5 DIIID β N DIIID Torque (Nm)
7 DIIID studies demonstration plasmas relevant to these scenarios: ITER Baseline Scenario (IBS) (RWM studies) ITER Steady State ITER I p (MA) 15 / 9 q Q 10 / 5 DIIID β N DIIID Torque (Nm) à Experiment à Modelling
8 Measure the approach to instability: MHD spectroscopy EXP MHD spectroscopy*: A rotating kinkresonant n=1 field is applied with a set of internal coils (Icoils), at f=10 Hz or f=20 Hz ß rotation frequency of the RWM à The plasma response amplitude increases close to a stability boundary à The phase shows a jump Used to probe the proximity to a stability limit Expand the analysis and modeling space to the stable side of the modes * Fasoli PRL1995 * Reimerdes PRL 2004
9 RWMs: slowly growing, slowly rotating kinks MOD The ideal kink instability, with a realistic (nonideal) wall model, is described by the RWM branch of the dispersion relation à slow growth rate of the order of τ wall (~2.5 ms in DIIID) The RWM is influenced by à pressure and current profile gradients (ideal MHD) à resonances between the plasma rotation and the thermal particles drift frequencies à nonresonant contributions from fastparticles (NBI ions in DIIID) In DIIID, RWMs Cause rotation and β N collapses in the highq min, highβ N SS plasmas
10 Drift kinetic effects are needed to describe the experimental observations MOD RWMs do not usually appear in fastrotating, low q min plasmas à kinetic damping of the RWM [Hu et al, PRL2004] γτ W = δw NW δw WW Ideal MHD RWM dispersion relation γτ W = δw NW +δw K δw WW +δw K Kinetic damping physics δw k ~ l ( ω ω E ) f ε n f ψ ez ω ω p ω b + iν eff ω E Precession frequency Bounce frequency Collision frequency Kinetic dependences may extrapolate unfavourably for low external torque and lower fraction of fast beamgenerated ions (ITER) à need to validate models for rotation and thermal/fast particles
11 MARSK model is being validated to predict the stability in unexplored regimes MOD Eigenvalue code, modified to solve for the response to an inhomogeneous forcing function ß External field from the Icoils The model includes  resistive DIIID wall geometry  rotation, T e, T i, n e from experiment  fastnbi ions with a Maxwellian slowing down distribution function  radially constant collisionality (for ions and electrons) *Y. Liu et al, Phys. Plasmas 15, (2008)
12 [IBS] MHD stability below the nowall limit, at zero torque ITER Baseline Scenario (IBS) (RWM studies) ITER Steady State ITER I p (MA) 15 / 9 q Q 10 / 5 DIIID β N DIIID Torque (Nm)
13 [IBS] Stable solution found at moderate to high torque EXP DIIID IBS demonstration discharges match  plasma shape (LSN)  q 95 = Q = 10 ß β N =1.8, H 98 =1 at q 95 =3 DIIID can match the predicted torque à Nm Solution non reproducible (50% of cases are unstable)
14 [IBS] At zero torque life is hard... EXP  Narrow operating point found at 1 Nm  Operation at 0 Nm remains elusive Operating on a marginal point à sensitive to small perturbations Ideal nowall limit β NW ~ Ideal withwall limit β WW ~ IBS constant β N ~ Nonideal effects à current profile, rotation, collisionality, resistivity?
15 [IBS] MHD spectroscopy shows that the plasmas are approaching a stability limit EXP Response amplitude increase Nonideal effects ß à Lower limits Phase jump at ~1215 krad/s à Typical of nowall limit crossing Response AMP (G/kA) Response PHI ( ) β N ~ β N ~ Phase jump NBI torque (Nm) NBI torque (Nm) Rotation at ρ~0.7 (krad/s)
16 [IBS] The plasma response trends indicate that nonideal effects are present EXP  At moderate rotation, the trends are consistent with the ideal model Plasma response amplitude (G/kA) β N /β lim Rotation at ρ=0.7 (krad/s)
17 [IBS] The plasma response trends indicate that nonideal effects are present EXP  At moderate rotation, the trends are consistent with the ideal model  At higher rotation the response is off trend à kinetic damping? Plasma response amplitude (G/kA) β N /β lim Rotation at ρ=0.7 (krad/s)
18 [IBS] The plasma response trends indicate that nonideal effects are present EXP  At moderate rotation, the trends are consistent with the ideal model  At higher rotation the response is off trend à kinetic damping?  At very low rotation, with ECH, higher response à collisionality? resistivity? Ideal MHD likely not sufficient to explain the trends Plasma response amplitude (G/kA) β N /β lim Rotation at ρ=0.7 (krad/s)
19 [IBS] MARSK reproduces only the higher rotation cases EXP  Collisionality is important to reproduce the higher rotation range correctly  MARS does not capture the large increase at very low rotation  The phase is overestimated by ~1520 Response amplitude(g/ka) MARSK w/o coll. MARSK w/ coll. NBI torque (Nm) Response phase ( ) NBI torque (Nm) (B r ) Rotation at ρ~0.7 (krad/s)
20 The path to high β N is a good platform to validate models ITER Baseline Scenario (IBS) (RWM studies) ITER Steady State ITER I p (MA) 15 / 9 q Q 10 / 5 DIIID β N DIIID Torque (Nm) Higher β N Higher q 95
21 Pressure (β N ) scan to cross the nowall β N limit EXP Increase the pressure with coip NBI power à fixed q95, li à Measure the plasma response
22 β N scan: It s crucial to assess the validity of the modeling results MOD Rotation has an impact on the response amplitude The rotation is not constant across the β N values à Sensitivity study: assess impact of rotation on the results
23 β N scan: MHDonly model does not reproduce approach to the nowall β N limit MOD Previous modelling* showed the MHD model without rotation has a pole at the nowall limit *Lanctot, PoP2010 Plasma Response Amplitude (GkA) Plasma Response Phase ( ) Experiment MHD only Kinetic Ideal model Model Nowall limit (without rotation) Nowall limit (without rotation) β N
24 β N scan: Drift kinetic model reproduces approach to the nowall β N limit correctly MOD Previous modelling* showed the MHD model without rotation has a pole at the nowall limit The pole is eliminated with the full kinetic model (thermal + fast ions) *Lanctot, PoP2010 Plasma Response Amplitude (GkA) Plasma Response Phase ( ) Experiment MHD only Full kinetic Kinetic Model Nowall limit (without rotation) Nowall limit (without rotation) β N
25 β N scan: Drift kinetic model reproduces approach to the nowall β N limit correctly MOD Previous modelling* showed the MHD model without rotation has a pole at the nowall limit The pole is eliminated with the full kinetic model (thermal + fast ions) Without fastion damping the pole reappears à 45% higher than expt The phase shift is still overestimated above the nowall limit ITER: very small fastion β from NBI à will the plasmas be (45%) more unstable? à Will the fast αparticles be enough to stabilize them? *Lanctot, PoP2010 Plasma Response Amplitude (GkA) Plasma Response Phase ( ) Kinetic Model Experiment MHD only Thermal+fast +45% Thermal Nowall limit (without rotation) ?? Nowall limit (without rotation) β N
26 β N scan: Precession and bounce drift frequencies are the main factors MOD The full model is necessary to reproduce the experiment
27 ITER Baseline Scenario (IBS) (RWM studies) ITER Steady State ITER I p (MA) 15 / 9 q Q 10 / 5 DIIID β N DIIID Torque (Nm) Higher β N Higher Torque
28 [SS] MHD stability is the main challenge for highβ N scenarios EXP  High rotation, β N <=3.6 à can be made passively stable  2/1 tearing modes arise on β N >3.6 flattop  They degrade the confinement significantly à loss of 2050% β N β N I p n=1 amplitude (G) , , Time (ms)
29 [SS] Tearing limits are strongly correlated with the ideal withwall limit MOD The tearing index Δ increases sharply at the ideal wall limit Modelling of the approach to the ideal limit:
30 [SS] Tearing limits are strongly correlated with the ideal withwall limit MOD The tearing index Δ increases sharply at the ideal wall limit High β N operation Operate with very large, very sensitive Δ? Modelling of the approach to the ideal limit: One solution is to increase the ideal limit:  broaden J and p  change the plasma shape Turnbull, PRL 1995 Turnbull, NF 1998
31 [SS] OFFaxis NBI used to broaden the pressure and current profiles The withwall β N limits of the OFFaxis cases are ~10% higher
32 [SS] Shape modifications can yield β limit ~6 MOD The withwall β N limits of the OFFaxis cases are ~10% higher Combined changes of outer gap and squareness: β lim 4.5 à 6 Withwall β N limit Upper squareness
33 [SS] The PEST3 model captures the approach to tearing instability PEST3 Δ Time series of Δ calculated* for experimental equilibria β N ~4 Higher β N >4 cases à Δ shows increasing trend towards the 2/1 mode β N ~ Time (s)
34 [SS] For stable plasmas, Δ decreases The stable cases can have high Δ values But show a stable or decreasing trend on the flattop β N ~
35 [Rotation scan] All the highβ N plasmas have high NBI torque MOD What happens at low rotation, high β N?  Experiment à decrease the rotation at fixed β N, q 95  Model à capture the rotation effects? fixed equilibrium and n e, T e, n i, P NBI, etc, from a DIIID plasma a selfsimilar rotation profile series Plasma rotation and drift frequencies Plasma rotation (krad/s)
36 Rotation effects above the nowall β N limit EXP Broad peak in the response at krad/s (~1% of the Alfvén velocity) Below the nowall limit (IBS) the trend is increasing Response AMP (G/kA) MHD spectroscopy Response PHI ( ) Rotation at ρ~0.6 (krad/s)
37 [Rotation scan] MARSK reproduces the response amplitude with fastions MOD MHD spectroscopy With thermal and fast ions, trend and amplitude are well matched...but the phase is underestimated by ~25% If the fastions damping is neglected, the results diverge (more) from the measurements Fastions destabilizing at highβ N? consistent with β N scan results... Response AMP (G/kA) Response PHI ( ) MARSK w/ fast ions MARSK w/o fast ions Rotation at ρ~0.6 (krad/s)
38 Summary and conclusions Modelling the approach to instability: how are we doing?  ITER Baseline Scenario:  Good match at moderate rotation  MARSK does not reproduce the high response at zero torque  Nowall limit crossing:  MARSK reproduces very well the response amplitude  The phase is overestimated at high β N  Steadystate scenarios:  PEST3 captures the approach to instability  No rotation dependence! Needed to extrapolate  The rotation dependence at high β N :  MARSK captures the amplitude trends  The phase trends are not reproduced as well
39 What physics can be added and may be relevant? Collisionality à New MARSQ: energy dependent collisionality operator Finite ion orbits? The present version of MARSK assumes a Maxwellian fastion distribution (experimental profile in ρ, but no v //, v perp dependence) à Neutral beam ions in DIIID are strongly anisotropic Large response at zero torque remains a puzzle... Experimental beamion distribution (NUBEAM)
40 EXTRAS
41 Currentdriven mode: The mode structure is similar to that of the pressuredriven mode The mode eigenfunction is a combination of the main harmonics m=2,3,4,5 The structure of the mode extends radially inward à not only at the edge Comparable to the pressuredriven mode Previously developed RWM feedback techniques and the low q optimizations can be applied to both currentdriven and pressuredriven, high β N modes F. Turco/IAEA 2014/St. Petersburg
42 MISK results for rotation scan
43 [IBS] MARSK reproduces only the higher rotation cases EXP  Collisionality is important to reproduce the higher rotation range correctly  MARS does not capture the large increase at very low rotation  The phase is overestimated by ~1520 Response amplitude(g/ka) MARSK w/o coll. MARSK w/ coll. NBI torque (Nm) Response phase ( ) (B p ) Rotation at ρ~0.7 (krad/s) NBI torque (Nm)
44 [IBS] MARSK reproduces only the higher rotation cases EXP
45 The Hybrid Regime Addresses the SteadyState Challenges With An Alternative Approach What is a hybrid? à Long duration, high confinement Hmode à More stable to 2/1 tearing modes Final J independent from sources Current density All external current driven in the plasma centre SS Highq min SS Hybrid No alignment issues Most efficient CD q relaxes to hybrid state q min 1 q 3/2 TM q=1 q= , Ideal MHD withwall limits are β limit 4.5 High q min present limits β lim ~ à predicted β lim ~5
46 The Highest β N Cases Are Limited By MHD At β N 3.6 à 2/1 tearing modes are avoidable At β N 4 à fishbonelike bursts, then 2/1 tearing modes à nonrecoverable isolated bursts: β N , τ 1 ms, f khz n=1 Amp (G) τ 50 ms, f~1015 khz The activity does not decrease with density à not fishbones? May be due to the large fraction of fast particles B dot B dot bursts Time (ms)
47 Hybrid plasmas reach fully NI conditions and β N =3.6 for ~2 τ R EXP Double null plasma shape β N τ R H98y , , P NBI (MW) P ECH (MW) Density (10 19 m 3 ) Stable to the 2/1 TM at β N ~3.6 Loop voltage ~ 0 for ~2 τ R Limited by NBI pulse duration V surf (mv) Time (ms)
48 The Scenario Is Sustained At High Injected Torque Lower Torque Degrades Confinement  1 neutral beam line added in counteri p direction (~4 MW)  Same β N, stored energy obtained Confinement decreases by ~20% for 35% lower T P NBI = 11 à 15 MW (35% increase) β N , P NBI (MW) 2/1 TM P ECH (MW) T NBI = 8.8 à 5.6 Nm (35% decrease) NBI torque (Nm) H 98y2 H 98y2 = 1.72 à 1.4 (20% decrease) Time (ms) 2/1 TM
49 With Present Confinement And n e, The DN Hybrid Is Consistent With an FNSF 6.7 MA Scenario INPUTS: R=2.49 m, B t = 6 T q 95 =6.2, ε=3.5 β N =3.66, n lin.av =4 DN 6.7 MA FNSF hybrid Plasma current (MA) scaled Impose I p = 6.7 MA Fix ν* H 98y2 =1.42 SCALED SCENARIO: With n/n G = 0.42 Drive 3.35 MA with ECH+NBI Need P CD = 75 MW P to sustain β N = 172 MW Central Temperature (kev) P INPUT (MW) Density (10 19 m 3 ) (f G = 0.42) Time (s) P CD (MW)
50 With Present Confinement And n e, The SN Hybrid Is Consistent With an ITER 9 MA Scenario INPUTS: R=6.2 m, B t = 5.3 T q 95 =6.2, ε=3.1 β N =3, n lin.av =3.2 SN 9 MA ITER hybrid Plasma current (MA) scaled Impose I p = 9 MA Fix ν* H 98y2 =1.49 Density (10 19 m 3 ) n G (f G = 1.17) SCALED SCENARIO: With n/n G = 1.17 Drive 4.5 MA with ECH+NBI Need P CD = 191 MW P to sustain β N à 175 MW Q = 7.1 Central Temperature (kev) P INPUT (MW) P CD (MW) Time (s)
51 With Present Confinement And lower n e, The SN Hybrid Is Consistent With an ITER 9 MA, Q=4.4 Scenario INPUTS: R=6.2 m, B t = 5.3 T q 95 =6.2, ε=3.1 β N =3, n lin.av =3.2 SN 9 MA ITER hybrid Plasma current (MA) scaled Impose I p = 9 MA Scale f GW H 98y2 =1.49 Density (10 19 m 3 ) n G (f G = 0.9) SCALED SCENARIO: With n/n G = 0.9 Drive 4.5 MA with ECH+NBI Need P CD = 112 MW P to sustain β N à 233 MW Q = 4.4 Central Temperature (kev) P INPUT (MW) P CD (MW) Time (s)
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